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Question

Determine the degree of each of the following polynomials.

(i) 4x5x2+6x32x

(ii) y2(yy3)

(iii) (3x2)(2x3+3x2)

(iv) 12x+3

(v) 8

(vi) x2(x4+x2)

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Solution

(i) 4x5x2+6x32x
Here, the highest power of x is 2. So, the degree of the polynomial is 2.

(ii) y2(yy3)
Here, the highest power of y is 5. So, the degree of the polynomial is 5.

(iii) (3x2)(2x3+3x2)=6x4+9x34x36x2=6x4+5x36x2
Here, the highest power of x is 4. So, the degree of the polynomial is 4.

(iv) 12x+3
Here, the highest power of x is 1. So, the degree of the polynomial is 1.

(v) 8
–8 is a constant polynomial. So, the degree of the polynomial is 0.

(vi) (x2)(x4+x2)=x2+x0=x2+1
Here, the highest power of x is 2. So, the degree of the polynomial is 2.


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